Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients (Case: H 0 > 0)

Hovik A. Matevossian (), Maria V. Korovina and Vladimir A. Vestyak
Additional contact information
Hovik A. Matevossian: Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333 Moscow, Russia
Maria V. Korovina: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
Vladimir A. Vestyak: Institute 3, Moscow Aviation Institute (National Research University), 125993 Moscow, Russia

Mathematics, 2022, vol. 10, issue 16, 1-26

Abstract: The main goal of this article is to study the behavior of solutions of non-stationary problems at large timescales, namely, to obtain an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients at large values of the time parameter t . To obtain an asymptotic expansion as t → ∞ , the basic methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of the Hill operator with periodic coefficients in the case when the operator is positive: H 0 > 0 .

Keywords: asymptotic behavior of solutions; second-order hyperbolic equation; periodic coefficients; Cauchy problem; Hill operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2963/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2963/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:16:p:2963-:d:890231

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().